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SM + W' and Z' at NLO in QCD

Contact Authors

Benjamin Fuks

LPTHE - CNRS - UPMC (Paris VI)

fuks AT lpthe.jussieu.fr

Richard Ruiz

University of Durham (IPPP)

richard.ruiz AT durham.ac.uk

Model Description

This effective model extends the Standard Model (SM) field content by introducing the massive vector fields W'+/- and Z' bosons, which are electrically charged and neutral, respectively. To remain model independent, couplings to SM gauge bosons and scalars are omitted.

Following Refs. [ 1, 2 ], the Lagrangian parameterizing the new vector bosons' couplings to up-type and down-type quark fields ui and dj is given by

Here, i and j denote flavor indices, PL/R
are the usual left/right-handed chirality projectors, VCKM is the CKM matrix,
and g and \theta_W are the weak coupling constant and mixing angle respectively.
We choose coupling normalizations facilitating the mapping to the reference Sequential Standard Model (SSM) Lagrangian {\cal L}_{\rm SSM} [ 3 ].
The real-valued quantities \kappa_{L,R}^q and \zeta_{L,R}^q
serve as overall normalization of the new interactions relative to the strength of the weak coupling constant.

The quantities \kappa_L^\ell are real-valued and serve as normalizations for
leptonic coupling strengths. As no right-handed neutrinos are present in the SM, the corresponding
right-handed leptonic new physics couplings are omitted (\zeta_R^\nu = \kappa_R^\ell = 0).

From our general Lagrangians, the SSM limit is obtained by imposing the coupling strengths to be equal to the SM weak couplings up to an overall normalization factor:

In the canonical SSM, the overall normalizations are further trivially fixed as

NLO in QCD Corrections

The above Lagrangian in the Feynman Gauge was implemented into FeynRules 2.3.10. QCD renormalization and R2 rational counter terms were determined using NLOCT 1.02 and FeynArts 3.8. Feynman rules were collected into a single UFO, available below.
In the UFO file, five massless quarks are assumed as well as vanishing off-diagonal CKM matrix entries.
For additional details, see [ 4 ] and references therein.
These additions permit tree-level calculations at LO and NLO in QCD, loop-induced calculations at LO in QCD, and NLO calculations matched to NNLL(Veto) resummation using MadGraph_aMC@NLO.

Validation

The model file was validated at NLO in [ 4 ] by comparing against Standard Model predictions and W' predictions from [ 5 ], as well as private LO and NLO calculations. See Table III of [ 4 ] for representative total widths that have been checked against analytic computation.